Find the solution set of 4x−3>9 and x+6>−2 .(1 point) Responses {x|x>3} left brace x vertical bar x greater than 3 right brace {3,−8} left brace 3 comma negative 8 right brace {x|x>−8} left brace x vertical bar x greater than negative 8 right brace The solution set is null.

Answer 1

To find the solution set of the inequalities \(4x - 3 > 9\) and \(x + 6 > -2\), we will solve each inequality separately.

1. Solving the first inequality: \[ 4x - 3 > 9 \] Add 3 to both sides: \[ 4x > 12 \] Divide by 4: \[ x > 3 \]

2. Solving the second inequality: \[ x + 6 > -2 \] Subtract 6 from both sides: \[ x > -8 \]

Now, we need to find the values of \(x\) that satisfy both inequalities \(x > 3\) and \(x > -8\). The more restrictive condition here is \(x > 3\).

Thus, the solution set is: \[ {x \mid x > 3} \]

Therefore, the answer is: \[ {x \mid x > 3} \]